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3 years ago

Complete the equation of the line whose y-intercept is (0, 5) and slope is -9. y =

1 answer:

5 0

You would just plug the values into the slope-intercept formula which is y=mx+b. m is representative of the slope, and b is representative of the y-intercept. The equation would be y=-9x+5

You might be interested in

Convert ( 4 , 300 ∘ ) to rectangular form.

Rasek [7]

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

According to the statement

we have given a coordinates of the rectangle and we have to find the polar coordinates.

So, For this purpose, we know that the

We Use the conversion formulas to convert from polar coordinates to rectangular coordinates which are

x = rcosθ

y = rsinθ

Substitute the given values in it then

x=(4)cos(300)

y=(4)sin(300)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

x=(4)cos(60) -(1)

y= - (4)sin(60) -(2)

And then

x=(4)cos(60)

x=(4)(1/2)

x = 2 -(3)

and

y= - (4)sin(60)

y= - (4)(√3/2)

y= - 2√3 -(4)

Replace (3) with (1) and (4) with (2)

then it becomes

x = 2 and y= - 2√3

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

Learn more about polar coordinates here

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6 0

1 year ago

A normally distributed population has mean 57,800 and standard deviation 750. Find the probability that a single randomly select

Stels [109]

Answer:

(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411

(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621

Step-by-step explanation:

We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; $\mu$ = 57,800 and $\sigma$ = 750.

Let X = randomly selected element of the population

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)

P(X <= 58,000) = P( $\frac{X-\mu}{\sigma}$ <= $\frac{58000-57800}{750}$ ) = P(Z <= 0.27) = 0.60642

P(X < 57000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{57000-57800}{750}$ ) = P(Z < -1.07) = 1 - P(Z <= 1.07)

= 1 - 0.85769 = 0.14231

Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .

(b) Now, we are given sample of size, n = 100

So, Mean of X, X bar = 57,800 same as before

But standard deviation of X, s = $\frac{\sigma}{\sqrt{n} }$ = $\frac{750}{\sqrt{100} }$ = 75

The z probability is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)

P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)

P(X bar <= 58,000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{58000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z <= 2.67) = 0.99621

P(X < 57000) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{57000-57800}{\frac{750}{\sqrt{100} } }$ ) = P(Z < -10.67) = P(Z > 10.67)

This probability is that much small that it is very close to 0

Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .

7 0

3 years ago

Negative three fourths plus negtive one half

Alexxandr [17]

The solution is -5/4= -1 1/4

8 0

3 years ago

Read 2 more answers

Let T be the plane-2x-2y+z =-13. Find the shortest distance d from the point Po=(-5,-5,-3) to T, and the point Q in T that is cl

GaryK [48]

Answer:

d=10u

Q(5/3,5/3,-19/3)

Step-by-step explanation:

The shortest distance between the plane and Po is also the distance between Po and Q. To find that distance and the point Q you need the perpendicular line x to the plane that intersects Po, this line will have the direction of the normal of the plane $n=(-2,-2,1)$ , then r will have the next parametric equations:

$x=-5-2\lambda\\y=-5-2\lambda\\z=-3+\lambda$

To find Q, the intersection between r and the plane T, substitute the parametric equations of r in T

$-2x-2y+z =-13\\-2(-5-2\lambda)-2(-5-2\lambda)+(-3+\lambda) =-13\\10+4\lambda+10+4\lambda-3+\lambda=-13\\9\lambda+17=-13\\9\lambda=-13-17\\\lambda=-30/9=-10/3$

Substitute the value of $\lambda$ in the parametric equations:

$x=-5-2(-10/3)=-5+20/3=5/3\\y=-5-2(-10/3)=5/3\\z=-3+(-10/3)=-19/3\\$

Those values are the coordinates of Q

Q(5/3,5/3,-19/3)

The distance from Po to the plane

$d=\left| {\to} \atop {PoQ}} \right|=\sqrt{(\frac{5}{3}-(-5))^2+(\frac{5}{3}-(-5))^2+(\frac{-19}{3}-(-3))^2} \\d=\sqrt{(\frac{5}{3}+5))^2+(\frac{5}{3}+5)^2+(\frac{-19}{3}+3)^2} \\d=\sqrt{(\frac{20}{3})^2+(\frac{20}{3})^2+(\frac{-10}{3})^2}\\d=\sqrt{\frac{400}{9}+\frac{400}{9}+\frac{100}{9}}\\d=\sqrt{\frac{900}{9}}=\sqrt{100}\\d=10u$

7 0

3 years ago

Simplify these expressions. a.2r+3+4r. b.8+3d+d. c.mn+ (-3mm)+6 d. 10s + (-10) + (-4s)

Maru [420]

Step-by-step explanation:

<em>Combine like terms</em>

a. 2r + 3 + 4r = (2r + 4r) + 3 = 6r + 3

b. 8 + 3d + d = (3d + d) + 8 = 4d + 8

c. mn + (-3mn) + 6 = (mn - 3mn) + 6 = -2mn + 6

d. 10s + (-10) + (-4s) = (10s - 4s) - 10 = 14s - 10

<em>Terms are called "like terms" if they have the same variable part (the same letters in the same powers). Like terms differ at most coefficient.</em>

7 0

3 years ago